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Article

Strong Chromatic Index of Outerplanar Graphs

by
Ying Wang
1,†,
Yiqiao Wang
2,‡,
Weifan Wang
3,*,§ and
Shuyu Cui
3
1
School of Mathematics and Information Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China
2
School of Management, Beijing University of Chinese Medicine, Beijing 100029, China
3
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
*
Author to whom correspondence should be addressed.
†
Research Supported Partially by NSFC (No. 12001156).
‡
Research Supported Partially by NSFC (No. 12071048) and Science and Technology Commission of Shanghai Municipality (No. 18dz2271000).
§
Research Supported Partially by NSFC (No. 12031018).
Axioms 2022, 11(4), 168; https://doi.org/10.3390/axioms11040168
Submission received: 4 February 2022 / Revised: 7 March 2022 / Accepted: 3 April 2022 / Published: 8 April 2022
(This article belongs to the Special Issue Graph Theory with Applications)
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Abstract

The strong chromatic index χs′(G) of a graph G is the minimum number of colors needed in a proper edge-coloring so that every color class induces a matching in G. It was proved In 2013, that every outerplanar graph G with Δ≥3 has χs′(G)≤3Δ−3. In this paper, we give a characterization for an outerplanar graph G to have χs′(G)=3Δ−3. We also show that if G is a bipartite outerplanar graph, then χs′(G)≤2Δ; and χs′(G)=2Δ if and only if G contains a particular subgraph.
Keywords: strong edge-coloring; strong chromatic index; outerplanar graph; bipartite graph strong edge-coloring; strong chromatic index; outerplanar graph; bipartite graph

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MDPI and ACS Style

Wang, Y.; Wang, Y.; Wang, W.; Cui, S. Strong Chromatic Index of Outerplanar Graphs. Axioms 2022, 11, 168. https://doi.org/10.3390/axioms11040168

AMA Style

Wang Y, Wang Y, Wang W, Cui S. Strong Chromatic Index of Outerplanar Graphs. Axioms. 2022; 11(4):168. https://doi.org/10.3390/axioms11040168

Chicago/Turabian Style

Wang, Ying, Yiqiao Wang, Weifan Wang, and Shuyu Cui. 2022. "Strong Chromatic Index of Outerplanar Graphs" Axioms 11, no. 4: 168. https://doi.org/10.3390/axioms11040168

APA Style

Wang, Y., Wang, Y., Wang, W., & Cui, S. (2022). Strong Chromatic Index of Outerplanar Graphs. Axioms, 11(4), 168. https://doi.org/10.3390/axioms11040168

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